V1 1 2 3 4 5 First Name Summary: V1 1 2 3 4 5 Last Name: First Name: ID: Section: Math 481a Midterm #1. March 16, 2005 Attention! Please, note that this is the closed book test. You are allowed to use a graphing calculator. In multiple choice, guessing is not penalized. In other problems, please, show all important steps in you solution. 1a. (5pt) If one is solving the root problem f(x) = 0 by the bisection method, and the initial interval [a, b] contains two roots, then the bisection method does not apply; the bisection section will find only one root; the bisection method will find the root which is closer to the middle of [a, b]; the bisection method will find the root that is farther from the middle of [a, b]; the bisection method will find both roots. 1b. (5pt) Which from the following is the MINIMUM requirements to guarantee that the fixed point equation g(x) = x has a solution on [a, b] g(x) is continuous on [a, b]; g(x) is continuous on [a, b], and the values of g(x) belong to [a, b] (g(x) maps [a, b] into itself); g(x) is continuous on [a, b], and the values of g(x) belong to [a, b] (g(x) maps [a, b] into itself), Collections: Physics